By Richard E. Crandall
Projects in Scientific Computation
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Contents
| Chapter 1: | Numbers Everywhere: Selected topics in numerical analysis |
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Numerical evaluation
› evaluation of famous constants
› evaluation of elementary functions
› special functions
Equation solving
› matrix algebra
› nonlinear equation systems
› differential equations
Random numbers and Monte Carlo
› generating random numbers
› numerical integration and Monte Carlo
› evaluation of elementary functions
› evaluation of elementary functions
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| Chapter 2: | Exploratory Computation: Collected intra- and interdisciplinary projects |
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Mathematical problems
› planar geometry problems
› symbolic manipulation
› real and complex analysis
Nature-motivated models
› neural network experiments
› genetic algorithms and artificial life
Projects from biology
› population models
› physiology, neurobiology and medicine
› molecular biology
Projects from physics and chemistry
› classical physics
› quantum theory
› molecules and structure
› relativity
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| Chapter 3: | The Lure of Large Numbers: Projects in number theory |
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Large-integer arithmetic
› testing the operations
› Prime numbers
› Mersenne primes
› primes in general
Fast algorithms
› fast multiplication
› fast mod, division, inversion
› other fast algorithms
Factoring
› factoring algorithms
› status of Fermat numbers
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| Chapter 4: | The FFT Forest: The ubiquitous FFT and its relatives |
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Discrete Fourier transform
› fundamental DFT manipulations
› algebraic aspects of the DFT
› DFT test signals
› direct DFT software
FFT algorithms
› recursive FFTs
› FFT indexing and butterflies
› complex FFTs, N a power of 2
› real-signal FFTs
› FFTs for other radices
› FFTs in higher dimensions
› applications of FFT
Real-valued transforms
› Hartley transform
› discrete cosine transform
› Walsh-Hadamard transform
› square-wave transform
Number-theoretic transforms
› exploring number theoretic transforms
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| Chapter 5: | Wavelets: Young arrivals in the transform family |
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Chords, notes and little waves
› windowed Fourier transform
› continuous wavelet transform
Discrete wavelet bases
› example wavelet expansions
› mother function and its wavelet
› wavelets of compact support
Discrete wavelet transform
› fast wavelet transform algorithms
› applications of fast wavelet transforms
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| Chapter 6: | Complexity Reigns: Chaos & fractals & such |
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Chaos
› quadratic map algebra
› bifurcation and chaos
› chaos models
› chaos, stability and Lyapunov exponents
› applications of chaos theory
Fractals
› theory of fractals
› visualization of fractals
› fractal Brownian noise
› measurement of fractal dimension
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| Chapter 7: | Signals from the Real World: Projects in signal processing |
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Data compression
› tour of lossless data compressors
Sound
› examples of sound processing
› examples of sound compression
Images
› examples of image processing
› image compression
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| Appendix |
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| Support code for the book projects |
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